Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+5y &= -8 \\ -2x+y &= -8\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-2x = -y-8$ Divide both sides by $-2$ to isolate $x$ $x = {\dfrac{1}{2}y + 4}$ Substitute this expression for $x$ in the first equation. $6({\dfrac{1}{2}y + 4}) + 5y = -8$ $3y + 24 + 5y = -8$ Simplify by combining terms, then solve for $y$ $8y + 24 = -8$ $8y = -32$ $y = -4$ Substitute $-4$ for $y$ in the top equation. $6x+5( -4) = -8$ $6x-20 = -8$ $6x = 12$ $x = 2$ The solution is $\enspace x = 2, \enspace y = -4$.